arXiv subjects
Publications and source records attributed to Alexander A. Chernitskii.
Nonlinear field model of extremal space-time film is considered. Its space-localized solutions in toroidal coordinates with periodic dependence on time are investigated. An accordance between these soliton solutions and leptons is considered.
The scalar field of extremal space-time film is considered as unified fundamental field. Metrical interaction between solitons-particles as gravitational interaction is considered here in approximation of a weak fundamental field. It is shown that the signature of metrics $\{-,+,+,+\}$ in the model formulation provides the observable gravitational attraction to a region with bigger energy density of the fundamental field. The induced gravitational interaction in the space-time film theory is applied to stars in a galaxy. The conception of galaxy soliton of space-time film is introduced. A weak field asymptotic solution for a galaxy soliton is proposed. It is shown that the effective metrics for this solution can provide the observable velocity curves for galaxies and explains their spiral structure. Thus a solution for so-called dark matter problem in the framework of space-time film theory is proposed.
The scalar field of space-time film is considered as unified fundamental field. The field model under consideration is the space-time generalization of the model for a two-dimensional thin film. The force and metrical interactions between solitons are considered. These interactions correspond to the electromagnetic and gravitational interactions respectively. The metrical interaction and its correspondence to the gravitational one are considered in detail. The practical applications of this approach are briefly discussed.
The concept of unified field theory is discussed. Two nonlinear field models with world volume type action are considered, namely extremal space-time film model and Born -- Infeld nonlinear electrodynamics. The natural appearance of two long-range fundamental interactions, electromagnetism and gravitation, in these field models is discussed. The quantum behaviour of the interacting solitons-particles is considered. The concept of quasi-bounding quantization in nonlinear field models is introduced.
Nonlinear field model of extremal space-time film is considered. Its space-localized solution in toroidal coordinates with periodic dependence in time is investigated. A field configuration having a form of the twisted lightlike soliton moving along the ring is considered. An iterative algorithm for obtaining the solution in the form of formal power series in one toroidal variable is proposed. It is discovered that the time dependence in the toroidal solution has a deeply embedded character. Thus the full energy and angular momentum of the solution converge at space infinity.
New exact solution class of Born -- Infeld type nonlinear scalar field model is obtained. The variational principle of this model has a specific form which is characteristic for extremal four-dimensional hypersurface or hyper-film in five-dimensional space-time. Obtained solutions are singular solitons propagating with speed of light and having energy, momentum, and angular momentum which can be calculated for explicit conditions. Such solitons will be called the lightlike ones. The soliton singularity has a form of moving two-dimensional surface or shell. The lightlike soliton can have a set of tubelike singular shells with the appropriate cavities. A twisted lightlike soliton is considered. It is notable that its energy is proportional to its angular momentum in high-frequency approximation. A case with one tubelike cavity is considered. In this case the soliton shell is diffeomorphic to a cylindrical surface with threads by multifilar helix. The shell transverse size of the appropriate finite energy soliton can be converging to zero at infinity. The ideal gas of such lightlike solitons with minimal twist parameter is considered in a finite volume. Explicit conditions provide that the angular momentum of each soliton in the volume equals Planck constant. The equilibrium energy spectral density for the solitons is obtained. It has the form of Planck distribution in some approximation. A beam of the twisted lightlike solitons is considered. The representation of arbitrary polarization for the beam with the twisted lightlike solitons is discussed. It is shown that the effect of mechanical angular momentum transfer to absorbent by the circularly polarized beam can be provided. This effect is well known for photon beam. Thus the soliton solution which have determinate likeness with photon is obtained in particular.
The description of gravitation in the framework of soliton interaction is considered for two nonlinear field models. These models are Born -- Infeld nonlinear electrodynamics and so-called Born -- Infeld type scalar field model. The last model can also be called the extremal space-time film one because of the specific form of the appropriate variational principle. Gravitational interaction is considered in the context of unification for all interactions of material particles. It is shown that long-range interaction of solitons of the models appears as force one and metrical one. The force interaction can be interpreted as electromagnetic one. The metrical interaction can be interpreted as gravitational one.
The nonlinear scalar field model of space-time film (Born -- Infeld type nonlinear scalar field model) is considered. Its spherically symmetrical solution is obtained. This solution gives the class of moving solitary solutions or solitons with the Lorentz transformation. We consider the distant interaction between such spheroidal solitons or spherons. This interaction is caused by the nonlinearity of the model. Starting from the static configuration with two spherons we show that the interaction under investigation is similar to electromagnetic one.
Electromagnetic soliton-particle with both quasi-static and quick-oscillating wave parts is considered. Its mass, spin, charge, and magnetic moment appear naturally when the interaction with distant solitons is considered. The substantiation of Dirac equation for the wave part of the interacting soliton-particle is given.
An axisymmetric space-localized solution of nonlinear electrodynamics is considered as massive charged particle with spin and magnetic moment. The appropriate solution for nonlinear electrodynamics with ring singularity is investigated. In view of this problem the system of toroidal waves in linear electrodynamics is considered. The problem with boundary conditions on the singular ring of the toroidal coordinate system is investigated. The boundary conditions are taken taking into account the conformity between the toroidal and cylindrical waves on the ring. In this case the singular ring looks like convolute axis of cylindrical system. The appropriate system of wave modes are obtained in an integral form with the help of source function.
We consider an approach to unification of the gravitational and electromagnetic interactions based on the existence of an effective Riemannian space in nonlinear electrodynamics. In the context of this approach, we discuss the possibility of screening the gravitational field.
Effective Riemann space effect of vacuum nonlinear electrodynamics is considered in the context of theory for unified gravitation and electromagnetism. The electromagnetic four-vector potential in the scope of Born-Infeld nonlinear electrodynamics model is considered as the unified field. The electromagnetic interaction appears naturally in the first perturbation order by the small field of distant material objects. The gravitational interaction appears naturally in the appropriate second order. In this case the effective metric components contain the corresponding energy-momentum tensor components for quick-oscillating electromagnetic field of the distant objects.
The axisymmetric static solution of Born-Infeld nonlinear electrodynamics with ring singularity is investigated. This solution is considered as a static part of massive charged particle with spin and magnetic moment. The method for obtaining the appropriate approximate solution is proposed. An approximate solution is found. The values of spin, mass, and magnetic moment is obtained for this approximate solution.
We consider the unification problem for the gravitational and electromagnetic interactions and its possible solution on the basis of the existence of an effective Riemannian space in nonlinear electrodynamics
An axisymmetric static solution of a nonlinear electrodynamics is considered as a massive charged particle with spin and magnetic moment. A linearization of the nonlinear electrodynamics around the static solution is investigated. The appropriate problem for linear waves around the static solution is considered. This wave part of the particle solution is considered to provide the appropriate wave properties for the particle. It has been found that the right (experimentally proved) formula for frequency of this wave appears theoretically for the static solution with ring singularity.
Nonlinear electrodynamics model in hypercomplex form is considered. Its linearization around a solution is obtained. The appropriate problem for linear waves around static dyon solution (SDS) of Born-Infeld electrodynamics is investigated. Two types of wave scattering on SDS are considered: dissipative (with momentum transmission from plane wave to SDS) and non-dissipative (for SDS imbedded to an equilibrium wave background). Resonance phenomenon in the problem is discovered and some resonance frequencies are obtained by using a numerical method. The form of resonance wave modes are discussed. The sum of a plane wave (as the elementary component of the wave background) with one resonance mode is considered. The appropriate energy density is investigated at infinity. The averaged energy density is demonstrated to have the term proportional to inverse radius. This fact allow to consider such field configurations as the cause of gravitational interaction, taking into account the effective Riemann space effect discovered in my previous works. A behavior of the linearized solution at origin of coordinates and the problem beyond the linearization are discussed.
The field nature of spin in the framework of the field electromagnetic particle concept is considered. A mathematical character of the fine structure constant is discussed. Three topologically different field models for charged particle with spin are investigated in the scope of the linear electrodynamics. A using of these field configurations as an initial approximation for an appropriate particle solution of nonlinear electrodynamics is discussed.
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to nonlinear Born-Infeld electrodynamics. Thus the four-vector field is considered as an electromagnetic potential. It is suggested that space-localized (particle) solutions of the nonlinear field model correspond to material particles. Electromagnetic and gravitational interactions between field particles appear naturally when a many-particle solution is investigated with the help of a perturbation method. The electromagnetic interaction appears in the first order in the small field of distant particles. In the second order, there is an effective Riemannian space induced by the field of distant particles. This Riemannian space can be connected with gravitation.